// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Rohit Garg <rpg.314@gmail.com>
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
#define EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H

namespace Eigen {

namespace internal {

/** \internal \returns the arcsin of \a a (coeff-wise) */
template<typename Packet>
inline static Packet
pasin(Packet a)
{
	return std::asin(a);
}

#ifdef EIGEN_VECTORIZE_SSE

template<>
EIGEN_DONT_INLINE Packet4f
pasin(Packet4f x)
{
	_EIGEN_DECLARE_CONST_Packet4f(half, 0.5);
	_EIGEN_DECLARE_CONST_Packet4f(minus_half, -0.5);
	_EIGEN_DECLARE_CONST_Packet4f(3half, 1.5);

	_EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);

	_EIGEN_DECLARE_CONST_Packet4f(pi, 3.141592654);
	_EIGEN_DECLARE_CONST_Packet4f(pi_over_2, 3.141592654 * 0.5);

	_EIGEN_DECLARE_CONST_Packet4f(asin1, 4.2163199048E-2);
	_EIGEN_DECLARE_CONST_Packet4f(asin2, 2.4181311049E-2);
	_EIGEN_DECLARE_CONST_Packet4f(asin3, 4.5470025998E-2);
	_EIGEN_DECLARE_CONST_Packet4f(asin4, 7.4953002686E-2);
	_EIGEN_DECLARE_CONST_Packet4f(asin5, 1.6666752422E-1);

	Packet4f a = pabs(x); // got the absolute value

	Packet4f sign_bit = _mm_and_ps(x, p4f_sign_mask); // extracted the sign bit

	Packet4f z1, z2; // will need them during computation

	// will compute the two branches for asin
	// so first compare with half

	Packet4f branch_mask = _mm_cmpgt_ps(a, p4f_half); // this is to select which branch to take
	// both will be taken, and finally results will be merged
	// the branch for values >0.5

	{
		// the core series expansion
		z1 = pmadd(p4f_minus_half, a, p4f_half);
		Packet4f x1 = psqrt(z1);
		Packet4f s1 = pmadd(p4f_asin1, z1, p4f_asin2);
		Packet4f s2 = pmadd(s1, z1, p4f_asin3);
		Packet4f s3 = pmadd(s2, z1, p4f_asin4);
		Packet4f s4 = pmadd(s3, z1, p4f_asin5);
		Packet4f temp = pmul(s4, z1); // not really a madd but a mul by z so that the next term can be a madd
		z1 = pmadd(temp, x1, x1);
		z1 = padd(z1, z1);
		z1 = psub(p4f_pi_over_2, z1);
	}

	{
		// the core series expansion
		Packet4f x2 = a;
		z2 = pmul(x2, x2);
		Packet4f s1 = pmadd(p4f_asin1, z2, p4f_asin2);
		Packet4f s2 = pmadd(s1, z2, p4f_asin3);
		Packet4f s3 = pmadd(s2, z2, p4f_asin4);
		Packet4f s4 = pmadd(s3, z2, p4f_asin5);
		Packet4f temp = pmul(s4, z2); // not really a madd but a mul by z so that the next term can be a madd
		z2 = pmadd(temp, x2, x2);
	}

	/* select the correct result from the two branch evaluations */
	z1 = _mm_and_ps(branch_mask, z1);
	z2 = _mm_andnot_ps(branch_mask, z2);
	Packet4f z = _mm_or_ps(z1, z2);

	/* update the sign */
	return _mm_xor_ps(z, sign_bit);
}

#endif // EIGEN_VECTORIZE_SSE

} // end namespace internal

} // end namespace Eigen

#endif // EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
